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Probabilistic Termination by Monadic Affine Sized Typing [chapter]

Ugo Dal Lago, Charles Grellois
2017 Lecture Notes in Computer Science  
We introduce a system of monadic affine sized types, which substantially generalise usual sized types, and allows this way to capture probabilistic higher-order programs which terminate almost surely.  ...  The proposed type system is powerful enough to type classic examples of probabilistically terminating programs such as random walks.  ...  Monadic Affine Typing Necessary?  ... 
doi:10.1007/978-3-662-54434-1_15 fatcat:z4gjpholmnedvgehfdu4m4542u

Probabilistic Termination by Monadic Affine Sized Typing (Long Version) [article]

Ugo Dal Lago, Charles Grellois
2017 arXiv   pre-print
We introduce a system of monadic affine sized types, which substantially generalise usual sized types, and allows this way to capture probabilistic higher-order programs which terminate almost surely.  ...  The proposed type system is powerful enough to type classic examples of probabilistically terminating programs such as random walks.  ...  Lemma 44 (Reducibility for Infinite Sizes) Suppose that i pos ν and that W is the value Proof. Suppose that i pos ν and that, for every n ∈ N, Nat i →ν,ρ[i →m+1] , so that  ... 
arXiv:1701.04089v1 fatcat:itbrvj52bbh3zl5fl72vvdg3ue

Graded Monads and Graded Logics for the Linear Time - Branching Time Spectrum

Ulrich Dorsch, Stefan Milius, Lutz Schröder, Michael Wagner
2019 International Conference on Concurrency Theory  
A combination of universal coalgebra and graded monads provides a generic framework in which the semantics of concurrency can be parametrized both over the branching type of the underlying transition systems  ...  We extract graded logics for a range of graded semantics on labelled transition systems and probabilistic systems, and give exemplary proofs of their expressiveness based on our generic criterion.  ...  We will see one case where M 0 is the distribution monad; then M 0 -morphisms are affine maps.  ... 
doi:10.4230/lipics.concur.2019.36 dblp:conf/concur/DorschMS19 fatcat:eld6nrsmnrhqnluzpr6cxklmlm

Convexity and Order in Probabilistic Call-by-Name FPC [article]

Mathys Rennela
2020 arXiv   pre-print
We conclude the present work with a discussion of the interpretation of (probabilistic) recursive types, which are types for entities which might contain other entities of the same type, such as lists  ...  Kegelspitzen are mathematical structures coined by Keimel and Plotkin, in order to encompass the structure of a convex set and the structure of a dcpo.  ...  The monad D ∞ (resp. the monad D ∞ ≤1 ) is the infinitary (sub)probabilistic discrete distribution monad on the category Set.  ... 
arXiv:1607.04332v5 fatcat:642kk5elmfc4neklpdzluuyqqe

A Language for Probabilistically Oblivious Computation [article]

David Darais, Ian Sweet, Chang Liu, Michael Hicks
2019 arXiv   pre-print
Probability regions support reasoning about probabilistic correlation and independence between values, and our use of probability regions is motivated by a source of unsoundness that we discovered in the  ...  Lambda Obliv is new in its consideration of programs that implement probabilistic algorithms, such as those involved in cryptography.  ...  Second, we prove that key invariants about probabilistic values are ensured by mixed typing.  ... 
arXiv:1711.09305v4 fatcat:whl6llee4vdtrmvor6flfcx2ea

Convexity and Order in Probabilistic Call-by-Name FPC

Mathys Rennela
2016 Logical Methods in Computer Science  
We conclude the present work with a discussion of the interpretation of (probabilistic) recursive types, which are types for entities which might contain other entities of the same type, such as lists  ...  Kegelspitzen are mathematical structures coined by Keimel and Plotkin, in order to encompass the structure of a convex set and the structure of a dcpo.  ...  The monad D ∞ (resp. the monad D ∞ ≤1 ) is the infinitary (sub)probabilistic discrete distribution monad on the category Set.  ... 
doi:10.23638/lmcs-16(4:10)2020 fatcat:lky72qwitvaxpiwmqjky44oju4

Graded Monads and Graded Logics for the Linear Time – Branching Time Spectrum [article]

Ulrich Dorsch, Stefan Milius, Lutz Schröder
2020 arXiv   pre-print
A combination of universal coalgebra and graded monads provides a generic framework in which the semantics of concurrency can be parametrized both over the branching type of the underlying transition systems  ...  We extract graded logics for a range of graded semantics on labelled transition systems and probabilistic systems, and give exemplaric proofs of their expressiveness based on our generic criterion.  ...  We will see one case where M 0 is the distribution monad; then M 0 -morphisms are affine maps.  ... 
arXiv:1812.01317v3 fatcat:ds6ktiukdje3bjxhnso2i2gqkm

Page 8491 of Mathematical Reviews Vol. , Issue 2002K [page]

2002 Mathematical Reviews  
Calude, Elena Calude and Karl Svozil, Com- putational complementarity for probabilistic automata (99-113); Rudolf Freund and Ludwig Staiger, Acceptance of w-languages by communicating deterministic Turing  ...  , Definability of total objects in PCF and related calculi (4-5); Peter Selinger, Categorical semantics of control (6-7); Thorsten Altenkirch, Representations of first order function types as terminal  ... 

A Core Quantitative Coeffect Calculus [chapter]

Aloïs Brunel, Marco Gaboardi, Damiano Mazza, Steve Zdancewic
2014 Lecture Notes in Computer Science  
This additional structure is used to express comonadic type analysis.  ...  In this work, we present a language RPCF inspired by a generalized interpretation of the exponential modality.  ...  A bounded exponential situation is affine if I is terminal in A. An affine bounded exponential situation is enough to interpret the typing rules of RPCF (Fig. 2) .  ... 
doi:10.1007/978-3-642-54833-8_19 fatcat:lfedilzrobewxbj55nogaeodj4

Intersection Type Distributors [article]

Federico Olimpieri
2021 arXiv   pre-print
We conclude by describing two examples of our construction.  ...  We first introduce a class of 2-monads whose algebras are monoidal categories modelling resource management.  ...  We set M RA x to be the denotation of M in the case where S is the linear resource monad. We define the size s (π) of a typing derivation π as the number of application rules that appear in it.  ... 
arXiv:2002.01287v5 fatcat:qo4c7vnx3nbldgsw6usfis63o4

Categories of Brègman operations and epistemic (co)monads [article]

Ryszard Paweł Kostecki
2021 arXiv   pre-print
families of monads and comonads.  ...  Further restriction of objects to affine sets turns Br\'egman relative entropy into a functor.  ...  Each agent corresponds to a family of resource theories of states of type (iii L ℓ Υ ,Ψϕ ), parametrised by ℓ Υ -closed ℓ Υ -convex sets of free states. 15 On the other hand, Pow(N ⋆ ) has a terminal  ... 
arXiv:2103.07810v1 fatcat:h5dint35snhj7htqvcvwln7oli

Towards a linear algebra of programming

José N. Oliveira
2012 Formal Aspects of Computing  
Specification vagueness and nondeterminism are captured by relations. (Final) implementations are functions.  ...  This paper puts forward a basis for a linear algebra of programming (LAoP) extending standard AoP towards probabilistic functions.  ...  This research was carried out in the context of the Mondrian project funded by the ERDF through the Programme COMPETE and by the Portuguese Government through FCT (Foundation for Science and Technology  ... 
doi:10.1007/s00165-012-0240-9 fatcat:n423lcj5abazzorgn34izg2t2q

Raising Expectations: Automating Expected Cost Analysis with Types [article]

Di Wang, David M Kahn, Jan Hoffmann
2020 arXiv   pre-print
Bound inference is enabled by local type rules that reduce type inference to linear constraint solving.  ...  This article presents a type-based analysis for deriving upper bounds on the expected execution cost of probabilistic programs.  ...  It applies an affine refinement type system, called ℓRPCF, to derive bounds on the expected worst-case cost for an affine version of PCF [Plotkin 1977] . ℓRPCF can be seen as a probabilistic version of  ... 
arXiv:2006.14010v2 fatcat:vi5l7ycbnzcvlj2eqykrlm6akm

Equivalence of Deterministic Top-Down Tree-to-String Transducers Is Decidable

Helmut Seidl, Sebastian Maneth, Gregor Kemper
2018 Journal of the ACM  
For our main result, we prove that equivalence can be certified by means of inductive invariants using polynomial ideals.  ...  Instead, for a family B of affine sets, the least affine set containing all B ∈ B is given by: B = aff( B).  ...  Each occurring affine subset of Q n is represented by a basis.  ... 
doi:10.1145/3182653 fatcat:ayyyao4j4ncfflbq6lboybjbru

Equivalence of Deterministic Top-Down Tree-to-String Transducers is Decidable

Helmut Seidl, Sebastian Maneth, Gregor Kemper
2015 2015 IEEE 56th Annual Symposium on Foundations of Computer Science  
For our main result, we prove that equivalence can be certified by means of inductive invariants using polynomial ideals.  ...  Instead, for a family B of affine sets, the least affine set containing all B ∈ B is given by: B = aff( B).  ...  Each occurring affine subset of Q n is represented by a basis.  ... 
doi:10.1109/focs.2015.62 dblp:conf/focs/SeidlMK15 fatcat:grhs3xh6qfazhfyp5hwl64gt7a
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